Erik Green registered 14 points, while Dave Dudzinski, Malcolm Miller and Justin Burrell each scored 10 for Holy Cross (20-13), which lost to American in the semifinals of the Patriot League Tournament.
Leland King netted 18 points and grabbed 11 rebounds, while Cedric Kuakumensah added 12 points and 12 boards for the Bears (15-14), who lost their fourth straight game.
Holy Cross used a 12-0 run to build a double-digit lead just before the midpoint of the first half and carried a 42-31 cushion into the break.
The Crusaders led 64-55 with just over five minutes to play following a Thompson 3-pointer, but the Bears roared back with a 10-4 swing to get within three on King's triple with seven seconds left.
Burrell then turned the ball over on the Crusaders' next possession, but Malachi Alexander blocked King's 3-point try with three seconds left to seal the victory for Holy Cross.